The dramatic upheaval in the top level of the Carter administration has produced a very conventional result - the strengthening of Cabinet links to key political constituencies.

The outcome promises to pay short-term political dividens for a president focused on a tough renomination and reelection struggle. But many observers think it also could have built-in problems for Jimmy Carter's professed goal of tighter, better-coordinated administration policymaking.

In the massive shuffle of players that came to at least a temporary close Friday, Carter has elevated officials who can help his political fence-building with such diverse and vital constituencies as the financial community, big business, blacks, women, mayors, Catholics, Jews, the West Coast and even the Eastern establishment press.

While no one in the White House would acknowledge publicly that 1980 constituency politics was a primary goal of the shakeup, a leading Democratic Party official said yesterday, "The president has put together about as solid a Cabinet as I have ever seen in terms of touching the bases."

The bases to which he referred are constituency groups vital to an electoral-college victory 15 months from now.

In taking this approach, Carter has altered the pattern of his first effort at Cabinet-building after the 1976 election. And to some extent he has contradicted his stated goal that, in the future, there will be a clearer central control of administration policy from the White House itself.

When the first set of Cabinet-level appointees was revealed by Carter in December 1976, University of California-Berkeley political scientist Nelson Polsby remarked that the new president's choices were, for the most part, "very tenuously linked to the interest groups that are the clients of their agencies."

The avoidance of those links seemed perfectly in character for a man who had campaigned by proclaiming proudly, "I owe the special interest groups nothing."

Yesterday, a senior member of the White House staff said that while Carter has continued to chastise "special interests" as president, "it's a fair point to say that he has moved closer to them with these new appointment."

"It's a shift of degree," he said, "and probably not a conscious thing. But we all know this is July of 1979" - and an election year is approaching.

In the original Carter Cabinet, only two people clearly symbolized the traditional constituencies of the departments they were named to head. Neither was touched by the recent shuffle.

Secretary of Agriculture Bob Bergland, a Minnesota farmer and influential former member of the House Agriculture Committee, has weathered a period of abuse and criticism and now is reaping the benefits of high farm prices and bumper crops, particularly in his native Midwest.

Secretary of Interior Cecil Andrus, the former governor of Idaho, was named to a post traditionally viewed by the West as its domain. Andrus has borne the brunt of bitter complaints about the administration's water, energy, natural resource and land policies but has been a loyal defender of the president's decisions.

As a prominent Utah Democrat said, "The only way Carter can curb the criticism in the West is by changing policies - not people. And if he's going to stick with his policies, Cec Andrus%) is probably as good a defender as he can find."

Bergland and Andrus were unusual in the original Carter Cabinet in another respect. They were the only non-college graduates in a group top heavy with academicians, experts and Washington insiders.

In the shuffle, Carter plainly has decided to put the premium on constituency support and political contacts, rather than on paper credentials or Washington experience.

The most obvious evidence of the change involves the mayors of America - one of the most influential groups in domestic politics. In the first Cabinet, they were shut out. In the new one, they emerged with two key spots.

For the first time since the Department of Housing and Urban Development was created in the Johnson administration, the mayors have one of their own nominated as its head.

Former New Orleans mayor Moon Landrieu, a former president of the U.S. Conference of Mayors, has been named to replace Patricia Roberts Harris. As a bonus, Portland, Ore., Mayor Neil Goldschmidt has been nominated as successor to Brock Adams as secretary of transportation.

Coincidentally, the two mayors being brought into the Cabinet are representatives of two of the most closely contested states in the 1976 election. Carter carried Louisiana by 73,000 votes - his second-smallest margin in the South - and lost Oregon by only 1,713 votes, the closest he came anywhere in the West to winning.

With Adams, a former Seattle congressman, leaving the administration in anger, Goldschmidt would maintain representation of that region in the Cabinet.

In addition, Landrieu, a Catholic, and Goldschmidt, a Jew, can serve as bridges to two constituencies that have been sources of major concern to the president's political advisers.

A potentially even more significant move in that direction is the implied promise of a Cabinet position for former governor Jerry Apodaca of New Mexico. Apodaca who lunched with the president last week, said afterward that "I have reason to know that I will probably be named to a Cabinet position."

White House officials said Apodaca is in line to become the first Cabinet-level secretary of education, if administration-backed legislation to create a department of education, passed in differing forms by the House and Senate, becomes law.

During his term as governor, Apodaca served as chairman of the Education Commission of the States, a group with strong links to state school officials.

More important, he would be the first Hispanic-American Cabinet member, and would give that politically emerging minority a spokesman in bilingual education, an area of policy that is one of its major concerns.

A Democratic Party official said, "It's impossible to see how Carter can carry Texas, New Mexico or California without a strong Chicano vote." adding that the "symbolic value of an Apodaca appointment" would be "a tremendous political asset."

The groups represented by Landrieu, Goldschmidt and Apodaca all have been courted heavily by the administration. But the Cabinet shuffle also has opened the way for an improvement of relations with the business and financial community, with which Carter often has been at odds.

Three changes are regarded favorably by Wall Street and big business:

The replacement of James R. Schlesinger, an often abrasive professional economist, as head of the Department of Energy, by Charles W. Duncan Jr., a businessman with strong connections in Georgia and Texas who had been serving as deputy secretary of defense.

The replacement of W. Michael Blumenthal, a successful but maverick businessman, as secretary of treasury, by G. William Miller, an equally successful but more conventional business executive who had been serving as chairman of the Federal Reserve Board.

The replacement of Miller by Paul A. Volcker, president of the Federal Reserve Bank of New York. The Volcker nomination particularly was hailed by the international financial community, and domestic businessmen expressed hope that Miller would be more influential with Carter on economic issues than Blumenthal had been.

In the legal community - another periodic target of Carter attacks - there was general approbation of the elevation of Deputy Attorney General Benjamin Civiletti to succeed retiring Attorney General Griffin B. Bell.

The appointment of the Marylander to replace the Georgian is regarded less as a political move than as a victory for professionalism within the Justice Department. Symbolically, it is advantageous to the administration to have Civiletti, an Italian Catholic, move into the Cabinet when another Italian Catholic, Health, Education and Welfare Secretary Joseph A. Califano Jr., has been fired. But Civiletti is not expected to play an active role in the 1980 campaign.

Ironically, another of Carter's appointments this week can be viewed as an overture to part of "the establishment" with which the president has been feuding: the news media.

Hedley Donovan, retired editor-in-chief of Time Inc., who was named a senior adviser to the president on foreign and domestic policy - the only major addition to the White House staff so far announced - is not only a longtime Carter admirer but also a man with a great reputation among the leaders of the communications industry.

That Carter reached out for his help at the same time that he has been criticizing the influence of the "establishment press," particularly in Washington and on the East Coast, suggests a pragmatic desire to come to terms with that constituency as well.

The Donovan appointment was interesting in another respect, because it symbolizes the subordination of Carter's stated principles of government to the practicalities of mobilizing for the political struggles ahead.

Ten days ago, Carter formalized Hamilton Jordan's role as the White House chief of staff, declaring that there was a need for greater coordination of his official family. But when he appointed Donovan, he specified that the new adviser - whose duties apparently are to be wide-ranging - will report directly to Carter, not through Jordan. No one at the White House bothered to explain the seeming contradiction, and the impression was left that Carter took Donovan on Donovan's terms.

The situation was similar with Harris, who moved from HUD to HEW to replace Califano. On the record, Harris and Califano are quite similar - both committed liberals, skilled in Washington bureaucratic warfare, with a demonstrated readiness to challenge the presidential staff and the Office of Management and Budget when their pet projects are threatened. Presidential adviser Robert S. Strauss, in fact, said last week that no one had engaged in more battles with Hamilton Jordan than Harris.

If a smooth-running, coordinated administration were the real goal of the Cabinet shuffle, it is unlikely that Harris would have been the obvious choice for HEW. There are many inside the White House who believe that, over time, she could prove to be as contentious as Califano.

But the Harris appointment provides Carter with constituency benefits that Califano could not match. In the past two weeks, she has made strong speeches defending Carter before the National Women's Political Caucus and the National Urban League conventions. Her standing with blacks and women's groups can be exploited frequently in coming months.

As an associate of Sen. Edward M. Kennedy (D-Mass.) has pointed out, Harris also offers Carter a form of political protection - especially on the national health insurance issue, which Kennedy has made the centerpiece of his possible challenge to the president.

"Kennedy could go toe-to-toe with Califano, with no holds barred," the Kennedy friend said, "because no one worried about Joe holding his own. And it made for great television.

"With Pat Harris, he's got to be a lot more careful, cautious, low-keyed. He remembers what happened during her confirmation hearings, and he'll have to handle her with kid gloves." Back in 1976, Sen. William Proxmire (D-Wis.) questioned Harris' credentials as a spokesman for the urban poor, and she responded with a dramatic recital of her own youth in segregated Washington that not only quieted Proxmire but gave her a public relations triumph with the television audience.

In reaching into such diverse constituencies to select Harris, Volcker, Landrieu, Goldschmidt and (prospectively) Apodaca for senior policy making posts, Carter may well have added to the long-term problems of coordinating administration policy.

In the past 30 months, when he experimented with decentralized Cabinet government, his policymakers were mainly people without strong constituencies.

Now, as he moves to centralize authority in the White House, he is bringing in people who can - if they choose - rally their own constituencies to battle for programs and policies Carter may not want.

But those problems are prospective and could be solved by another Cabinet shuffle if Carter is reelected in 1980. Meantime, he enjoys the immediate benefits of their constituency relationships.

Ironically, however, members of the new group seem even weaker than their predecessors in one area where Carter has been having serious trouble - Congress.

Duncan begins at the Energy Department without the scars Schlesinger picked up in the battles of the past 30 months, but Civiletti, Miller and Volcker have no obvious advantages over their predecessors as salesmen of Carter programs on Capital Hill. Many observers think the chances of divergence on economic policy between the administration and the independent Fed may be greater with the Miller Volcker lineup than with Blumenthal-Miller.

In Landrieu, the administration is acquiring an effective political operator who enjoys a good personal relationship with Senate Finance Committee Chairman Russell B. Long (D-La.), a key legislator. Landrieu knows his way around Congress from his role as a leading lobbyist for enactment of the general revenue-sharing program in 1972.

But if he represents advantages over Harris, she is, on the record, a long step behind Califano in her knowledge of HEW programs and of the intricate relationships within the bureaucracy and on Capitol Hill on which those programs turn.

As for Transportation, Adams was able to exploit his knowledge of Congress, gained during 12 years in the House, in a way that Goldschmidt cannot be expected to match.The Portland mayor served briefly as a Senate aide and is a personable and bright executive, but he essentially will be starting from scratch with Congress.

What this suggests is that Carter is less concerned about substantive progress on his programs in the year between now and the Democratic convention than he is in securing a political base for renomination and reelection.

But if that is the case, it would appear the Cabinet shuffle is incomplete. The tilt is heavily toward the South, where Carter's personal strength is less diminished than in any other part of the country. Counting Ambassadors Andrew Young and Strauss, who sit with the Cabinet, six of the 14 members, plus most of the White House senior staff, are southerners.

There is a marked under-representation of domestic political figures from the Northeast or California - the areas from which Carter's nomination challenge is most likely to arise in the form of Kennedy or California Gov. Edmund G. (Jerry) Brown Jr.

Organized labor - a key element in the Democratic coalition - still has no one in or close to the top level of decisionmaking.

The obvious targets for change, if the constituency principle were applied, would be the departments of Commerce and Labor.

In Commerce, two North Carolinians, Secretary Juanita M. Kreps and Undersecretary Luther H. Hodges Jr., represent a geographical and political base so narrow it is almost unprecendented in Cabinet history.

In Labor, Secretary F. Ray Marshall of Texas, like Kreps and the departing Schlesinger an academic economist, holds a spot that could be a constituency prize.

As yet, there is no indication of impending changes in those departments. But even if the shakeup stops where it is, Carter will have demonstrated that the election cycle can move even the most resistant of presidents to acknowledge the importance of constituency politics. CAPTION: Picture, "The president has put together about as solid a Cabinet as I have ever seen in terms of touching the bases." "It's a shift of degree and probably not a conscious thing. But we all know this is July of 1979."